To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. TreatmentObservationA20302533B22262028C40302822 Note: rearrange this to (columns) in excel: A B C20 22 4030 26 3025 20 2833 28 22The test statistic to test the null hypothesis equals Group of answer choices19.2313.131.059.944
Question
To test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. TreatmentObservationA20302533B22262028C40302822 Note: rearrange this to (columns) in excel: A B C20 22 4030 26 3025 20 2833 28 22The test statistic to test the null hypothesis equals Group of answer choices19.2313.131.059.944
Solution
To test whether there is a difference between treatments A, B, and C, we can use a one-way ANOVA (Analysis of Variance). Here are the steps:
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First, input the data into Excel. Arrange the data in columns as follows:
A B C 20 22 40 30 26 30 25 20 28 33 28 22
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Next, we need to calculate the means of each treatment group. In Excel, you can use the AVERAGE function for this.
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Then, calculate the overall mean (grand mean), which is the mean of all observations regardless of the treatment group.
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Calculate the sum of squares between groups (SSB), which measures the variability between the groups.
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Calculate the sum of squares within groups (SSW), which measures the variability within each group.
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Calculate the mean square between groups (MSB) by dividing SSB by the degrees of freedom between groups (k-1, where k is the number of groups).
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Calculate the mean square within groups (MSW) by dividing SSW by the degrees of freedom within groups (N-k, where N is the total number of observations).
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The test statistic for the ANOVA F-test is the ratio of MSB to MSW. This is the value that you will compare to the critical value from the F-distribution table to decide whether to reject the null hypothesis.
Without the actual calculations, I can't provide the exact test statistic. However, the steps above should guide you on how to calculate it using Excel.
Similar Questions
o test whether or not there is a difference between treatments A, B, and C, a sample of 12 observations has been randomly assigned to the 3 treatments. You are given the results below. TreatmentObservationA20302533B22262028C40302822 Note: rearrange this to (columns) in excel: A B C20 22 4030 26 3025 20 2833 28 22The null hypothesis is to be tested at the 1% level of significance. The null hypothesis Group of answer choicesshould be revisedNo answer text provided.should not be rejectedshould be rejected
You obtained a significant test statistic when comparing three treatments in ANOVA. What is the conclusion?
In a study, subjects are randomly assigned to one of three groups: control, experimental A or experimental B. After treatment, the mean scores for the three groups are compared. The appropriate statistical test for comparing these means is:
Assuming the experiment was balanced: the number of different treatments used in the experiment, and the number of subjects (separate observations) for each treatment wereGroup of answer choices5 subjects on each of 4 treatments5 subjects on each of five treatments6 subjects on each of 4 treatments6 subjects on each of 5 treatments30 subjects on each of 4 treatments
A cosmetic company wanted to demonstrate the benefit of using their skincare for dark skin treatments. A sample of six was obtained, and each participant used it for 30 days. After 30 days, the scores were as follows:ParticipantBefore treatmentAfter treatment117222161931921415175121861318Is there any significant difference after 30 days? Use α = 0.05.a.Use paired t-test and there is a difference after 30 days of treatment.b.Use ANOVA test and there is a difference after 30 days of treatment.c.Use Z-test and there is a difference after 30 days of treatment.d.Use 2-sample t-test and there is a difference after 30 days of treatment.
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